martillo

Not so easy, you must have a specific area to consider what depends on each case in particular to solve. S-B law is general and applies to any case. More important than that, do you really pretend to solve the energy rates with Newton Second Law of force? I don't think you could solve the thing that way. You know, Boltzmann had to develop the concept of entropy and find his laws of statistical mechanics to solve the thing. You can't bypass over all that subject that way.

Nope. From Wikipedia: The Stefan–Boltzmann law, also known as Stefan's law, describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan, who empirically derived the relationship, and Ludwig Boltzmann who derived the law theoretically. For an ideal absorber/emitter or black body, the Stefan–Boltzmann law states that the total energy radiated per unit surface area per unit time (also known as the radiant exitance) is directly proportional to the fourth power of the black body's temperature, T: The constant of proportionality, �, is called the Stefan–Boltzmann constant. It has a value σ = 5.670374419...×10−8 W⋅m−2⋅K−4. In the general case, the Stefan–Boltzmann law for radiant exitance takes the form: where � is the emissivity of the matter doing the emitting. The emissivity is generally between zero and one, although some exotic materials may have an emissivity greater than one. An emissivity of one corresponds to a black body. and it is specifically explained: The radiant exitance (previously called radiant emittance), �, has dimensions of energy flux (energy per unit time per unit area), and the SI units of measure are joules per second per square metre (J⋅s−1⋅m−2),

I will answer now that question that surged some time ago: The answer is that the question is wrongly formulated. Stefan-Boltzmann law states that the energy density of the radiation of a system at a given temperature T is proportional to T4 while the heat energy transfer by conductivity is linearly proportional to T. The point is that they are different things and cannot be compared. They have different units. The question must be: If the radiance depends on T4 then why the energy transfer depends linearly on T only? I don't have to develop any formula for that, Boltzmann already solved the problem long time ago with his concept of Entropy. Boltzmann found the "fundamental hypothesis in statistical mechanics": This formula relates the micro states of the system (micro regions in the system) with the macro state of the system. It works under certain conditions like that all the micro states are equal and equally probable in the system. All the formulas of Thermodynamics can be derived from this formula. The Second Law of Thermodynamics is: and the Fundamental Thermodynamics Relation is: The other equations of Thermodynamics are derived form these equations and are all linear with T. The energy transfer we are thinking on is governed by these laws giving the linearity between dQ and T.

According to the Snell refraction formula it is so, we have: v1/v2 = n2/n1 I don't know if in some case the formula is not verified, may be other effects could be present. F.i. note that refraction happens at certain angles of incidence only.

Each material has its own spectrum of absorption and emission depending on the spectrum of its atoms. Also the molecular structure and the lattice plays a role, f.i. the number of atoms the photons encounter in their way through depends on the density of the material and so could be more or less time delays and so different velocities and different intensities (quantity of photons) passing through the material. And it is that way. The time delay depend on the frequency and this the basis for the functioning of prismas presenting different angles of refraction of the incident light for different colors (frequency). This is the Newton's experiment with light.

The question is: I could understand the need of a virtual particle as field propagator to explain the action at a distance of forces at far distances where the fields seem to vanish. I don't get why the need of a virtual particle in very close interactions. If the particles have an EM field they can directly interact through an EM force that would exist between them so, why the need of a mediating extra particle to represent this EM force? Sorry, I was editing the post and now it appears after your answer. I don't know why.

I have given a wrong answer. The same material can present different velocities in transmitting "light" or "heat". Glass for instance is an excellent light transmitter, it is transparent to light while a very bad heat transmitter, it is an insulator to heat. The difference is in the frequency of the photons involved. "Light" frequency is in the optical range while "heat" is mainly in the infrared range. Glass is an excellent transmitter in the optical range while a very bad transmitter in the infrared range. I must answer now why this happens with photons? It is because the glass' atoms cannot absorb the relative high energetic photons and they pass through the lattice or are reflected while they can well absorb and emit quite all the less energetic photons of heat. Now, how is that? Well, the absorption of photons by atoms depend on the available levels of energy in the atoms according to their particular characteristic energy spectrum with their characteristic levels of energies. I must also explain how the velocity of light in the glass is anyway less than in vacuum and this is because the light's photons pass through the lattice but have another interaction with atoms rather than absorption and emission. The interaction would be elastic collisions in which the photons are slowed down. The photons have an EM field which interacts with the EM field of the atoms with an EM force between them. The force act braking a bit the photons at first while accelerating them again after but a delay of time is involved in this process.

In both cases the velocity is slowed down because of the time delay of the same absorption/emission interaction of photons with the atoms. The velocity is different just depending on how much atoms the "light"/"heat" had interacted with before reaching the end.

Rare? What is actually rare is the "laser cooling" effect. I was referring to no direct observation. Heat transfer is mediated by photons and of course the photons responsible for the transfer must travel in the direction of flow at any place. I only predicted a time delay when an atom absorb a photon and a posteriori emit a photon. Valid for "light", "heat" whatever energy flow through a material substance composed by atoms.

It's a bit difficult to discuss with you when you instantaneously think in a possible objection and just post a few words about it without much care. I dedicate time and effort to understand what you are saying trying to get the real key point and answer appropriately and as precisely as possible. I was talking about the conservation of momentum in the photons with no net change in the momentum of the atom. The photons cannot be observed. I'm giving an explanation compatible with the observational evidence that is known about heat transfer and so my explanation is factible. If not give an observational evidence against it. As I said in the case we are analyzing of heat transferring of two bodies there is a preferred direction of flow and so that is what happens while quite no "laser cooling" effect is present. Not at all. I didn't predict any velocity. I just explained the known refractive velocity you provided to be less than c.

Isolated atoms don't "remember" the direction of the incoming photon, the probability is symmetric I agree. That's why I preciselly mentioned: "Then if I consider some little time after the atom emit other photon of the same kind -I mean same energy and same momentum absolute value (this what I call re-emission of a photon)- ". I after added the condition that: "and also in the same direction then the energy and momentum are both conserved." So I reasoned at the inverse: If the absorption and posterior emission of a photon happens in the same direction then energy and, particularly for us now, the momentum is conserved. We are analyzing the conduction of heat through a conductor between two bodies, right? We are analyzing how the heat flows in the direction of one body to the other one. When applying the Thermodynamics laws it is considered this flow between the two bodies and assuming there is no loss of heat so, in this case, there is a preferred direction of heat conduction. I'm explaining then, with my approach, how this directional flow happens with the mediating photons proposed. As I said in principle the atom doesn't "know" the difference. It is the inverse reasoning: if photons are emitted in the same direction as the absorbed one then there is no net effect in the momentum of the atom and so it "transmit" the energy in that direction and "laser cooling" effect does not take place. Now if photons are not emitted in the same direction then is right to say that then some "laser cooling" effect could take place. And how do you explain that slower velocity? I explain it through the absorption with posterior delayed emission of photons.

Well, I need to precisely define certain concepts here. Photons absorption involves energy absorption by the atom and a force on the atom due to the momentum conservation, right? Then if I consider some little time after the atom emit other photon of the same kind -I mean same energy and same momentum absolute value (this what I call re-emission of a photon)- and also in the same direction then the energy and momentum are both conserved. This is what I really meant while saying that the photons could "pass through" the atoms maintaining their original momentum. Now as a photon is emitted with same momentum it has exerted a force back opposite to that force in the absorption. The net momentum change on the atom is zero. This atom had no net effect as needed when cooling an atom by laser as you say. This does not mean laser cooling would not work. This mean that this atom in particular was not cooled. As you say laser cooling does actually imply a non zero net change in the momentum of the atom. It is just that this is not what happens in the atoms in the heat conducting process. Now you would ask for some experimental evidence about this process I described as you commented: As an evidence on that the photons' "passing through" the nucleus of atoms actually happens by the absorption with posterior emission of a photon of the same energy and momentum process I would mention that certain time delay is needed to this process take place. If not, if a photon would really pass through an atom practically unaltered this time delay would be negligible since the dimension of the nucleus would be negligible. Now, that time delay effect in each atom of the sequence of atoms involved in the path of the linear transmission of the heat I consider, is easily observed in practice as the heat transmission happens in a much slower velocity than the velocity of the photons. The heat transferring happens with the accumulation of all the delays of all the atoms in the sequence of the path and so the observable delay in the heat transmission in the total path. Strong challenge to me I must say. I will make my try, please give me some time. I'm reading your two recent posts now. Please tell me what is meant by "cross section" when describing "cross sections of the photons/phonons scatterings".

Sorry. I was posting just another mistake here. Deleted.

Good comment about real, quasi and virtual particles. I have now the intuitive concept that the quasi particles could come just because of a misunderstanding in the behavior of photons which could give the same cause for the considered behaviors on the interactions between real particles in QFT. I can imagine now that in the future all those quasi particles could be found as just particular instances of real photons. I have a better concept about them now. Virtual particles as fields propagators is something different. I think they come into place to substitute the classic concept of action at a distance of forces introducing also a delay in the action due to their finite velocity. I'm continuing the classical approach of instantaneous action a distance of the fields. I think I have made an important advance in this direction but this would be something off topic here in this thread. I hope to not need to use the QFT format. I like algebra but not in the format of tensors. May be just because I didn't dedicate time to them, I admit.

I have read the subject at Wikipedia and there it is said that laser cooling works due to the Doppler effect on moving atoms only. It is said that static atoms are not affected by the laser beam and they pass through the atoms maintaining their original momentum. For me a photon cannot just pass through the nucleus of an atom but their photons are absorbed and re-emitted while the momentum is maintained. The atoms in a metal lattice are stationary and so they can absorb and re-emit photons with that Doppler effect which maintain their original momentum as I have sustained. Conduction involves two bodies with some temperature each. This heat transfer is governed by the Thermodynamics laws in which the energies are proportional to KT and the heat transfer is linearly proportional to the temperatures' difference. A metal conductor acts just as a perfect mediator between the bodies for the heat transfer and so its conductance present the same linear proportionality in T. Not perfect conductors would present a gradient of temperature inside and their conductance would not present a linear relation with T. Vacuum is one such type of conductors in which the heat transfer presents a relation to T4.

The atom doesn't "know" that but momentum must be conserved so if the atom absorbs a photon coming in one direction it will "try" to re-emit it in the same direction. I mentioned "try" because the entire lattice will affect the emission direction and this way the path could curve. Conservation of momentum would play an essential role in the formation of the "linear" paths of conduction inside the metal. Other subject I must mention is that while an atom is not able to emit a photon it would be not able to absorb other photon and the same would happen with all the atoms in the entire path of absorption/re-emission I mentioned. This means that if in a conductor the conductance is broken at one of its ends it would not be able to absorb more photons in the other end and it would just reflect the incoming photons stopping the conduction of the heat from this side. I appreciate your comment but I have another very ambitious plan. I pretend to to not enter in the "Wave Mechanics Theory" which is about half of the broad "Quantum Physics Theory" as far as I could. I must mention the following: The mediator particle is important to me. My intention is to work with known real particles and not any virtual particle which are for me a mathematical artifice to make the things work (they have never been proved to really exist). They have the value to maintain the thing within the particles-like' model and not invoke the wave-like model of them which is also something of my interest but I pretend a model without them.

I think I can handle that. Where do you think I should focus the attention now?

Thanks for the comment. At least I'm moving forward I think.

Ok so, do I have the equivalent of conductance with phonons with this my photons approach?

I think I already got it in the right way in my approach. Let me try to explain it now. I have said that diffusion of photons, travelling inside a lattice structure would be the process of the conductance but I think now this was not the right thing. Bad tentative I admit. First scenario: thermal radiation: I consider this currently perfectly described by the Planck and the Stefan-Boltzmann laws applied to black body radiation with the necessary adjustments when applied to real bodies in practice. Radiation would be far not good in transmitting heat as the metals conductance is. Second scenario: thermal conductance: The situation is, we would have a "source" of heat emitting photons in direct contact to the crystalline lattice of a metal conductor connected by direct contact to a target "sink" of heat at its end. I'm considering now that the atoms of the lattice can absorb and re-emit photons quite instantaneously to the next atom of a linear path (not necessarily straight, it could be curved) in the lattice. This way the photons in one end can quite instantaneously be transmitted to the other end of the conductor. The capacity of conduction of the lattice would depend on the capacity of the atoms to absorb and re-emit photons to their other side which would be high in metal lattices. This the explanation for the excellent conductance of metals. Third scenario: Vacuum gap between two conductive materials as an insulator: A vacuum gap involves the surfaces at the end of the lattices' structures of two conductive materials. The point is that the atoms at those surfaces have no next atom to re transmit their absorbed photons on the other side. This way the conductance is lost. They could only radiate photons but this is the case of the first scenario which have much less capacity of heat transfer than the second scenario. This explains the insulation capacity of a vacuum gap. I hope this explanations could work for you at least as just a possibility to be taken into account.

OK, I have made a serious mistake, I admit. I was badly wrong when I said: I must have a good answer, based in my new approach, to the case of why a vacuum gap acts as a so good thermal insulator, of course. The thing became something very interesting for me. I should also have to explain why and how heat is so well transferred in the conductance of metals. You don't need to answer so ironically to that mistake. While true I graduated in Electrical Engineering and not in Physics, I'm in the Physics' area since lot of years ago although in an auto didactic way, that's true. You are ironic because I'm proposing a new approach and think this is something not right. For you there's no errors at all in all the already developed modern Physics. I'm strongly interested in the problem you presented now. I don't have a proper answer at this time but I'm thinking about. The case is a new challenging problem for me now. I hope I could arrive to the right answer not taking too long. Wait, a good idea to work on has just knocked my mind. Let me some time to present it properly.

But the energy transfer is always linear in the difference of the temperatures. dQ = CdT. The energy of a radiation at some place is given by S-B Law at a thermal equilibrium. Energy transfer involves difference in temperatures and so no thermal equilibrium. The energy transferred is directly proportional (linear) in the difference in temperature (assuming no loss in the transfer). The vacuum gap makes lot of difference in the conductance. In the gap there's no lattice so the emitted photons from one side don't follow the same diffusion pattern of the solids. They can just reflect while hitting the other solid surface, diffraction can happen etc. The conductance is lost.

No, heat transfer is governed by the laws of Thermodynamics whatever the origin of the heat through the linear, as you say, inter relations between Q, H, U, S and T. Heat transfer is always proportional to the difference in two temperatures. The value of each temperature is what is determined by the Stefan-Boltzmann Law. I don't know about that case. Can you provide more details? As for now I have no idea of what you are talking about. May be in the future, who knows. That is the current interpretations of things. I'm beginning to work in a new approach now. You can't expect I would have already found the alternative explanation for everything at this time.

Photons' absorption and emission. Electrons' energy levels in atoms. Photoelectric effect. Compton scattering. What else do you need? As I already said many times temperature is a magnitude related to the intensity of the radiation present. Is related to the quantity of photons passing through an area of space in relation to the interval of time and the area. The relation is given by the Stefan- Boltzmann Law Pot/A = σT4.

I always thought in heat transferring as a flow of photons. If not, how do you think thermal energy is transferred from one body to another one? The sun, for instance, it warms earth surface radiating photons through empty space. This way I think in temperature as a magnitude related to the intensity of the radiation of photons. Black body radiation is a radiation of originally called "quanta" by Planck and after photons by Einstein I think. So it is natural for me to think in heat as a flux of photons and temperature a way to measure their intensity. The model I'm working matches with this viewpoint. My approach focuses on how the energy is transferred, not in how it is contained. In the Kinetic Theory the energy is contained as vibrations of the atoms/molecules, I think it is not the case. I consider the theory of the electrons' levels of energy in the atomic electromagnetic structure well cover how the energy is contained by atoms. I mean the energy is stored in the electromagnetic fields of the atoms, not in mechanical vibrations.